Middle English short, from Old English sceort, scort "of little length; not tall; of brief duration," probably from Proto-Germanic *skurta- (source also of Old Norse skorta "to be short of," skort "shortness;" Old High German scurz "short"), from PIE root *sker- (1) "to cut," on the notion of "something cut off."
Compare Sanskrit krdhuh "shortened, maimed, small;" Latin curtus "short," cordus "late-born," originally "stunted in growth;" Old Church Slavonic kratuku, Russian korotkij "short;" Lithuanian skursti "to be stunted," skardus "steep;" Old Irish cert "small," Middle Irish corr "stunted, dwarfish," all considered to be from the same root.
Of memories from mid-14c. The sense of "not up to a required standard or amount" is from late 14c.; that of "not far enough to reach the mark" is by 1540s, in archery; that of "having an insufficient quantity" is from 1690s. The meaning "rude, curt, abrupt" is attested from late 14c. The meaning "easily provoked" is from 1590s; perhaps the notion is of being "not long in tolerating."
Of vowels or syllables, "not prolonged in utterance," late Old English. Of alcoholic drinks, colloquially, "unmixed with water, undiluted," by 1839, so called because served in small measure.
Short rib "asternal rib, one of the lower ribs," which are in general shorter than the upper ones, is from c. 1400. Short fuse in the figurative sense of "quick temper" is attested by 1951. Short run "relatively brief period of time" is from 1879. Short story for "work of prose fiction shorter than a novel" is recorded by 1877. To make short work of "dispose of quickly" is attested from 1570s. Phrase short and sweet is from 1530s. To be short by the knees (1733) was to be kneeling; to be short by the head (1540s) was to be beheaded.